2013/09/27 by Jochen Koenigsmann, Koenigsmann, Jochen
Mathematics · #12E30 #12L05 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.1309.7138
openalex publication_date 2013/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we give a negative answer to Abraham Robinson's question whether a finitely generated extension of an undecidable field is always undecidable. We construct 'natural' undecidable fields of transcendence degree 1 over Q all of whose proper finite extensions are decidable. We also construct undecidable algebraic extensions of Q that allow decidable finite extensions.